Due to escalating demands for spectrum resources, efficient use of bandwidth resources is a key parameter in design and realization of communication systems. Commonly used technologies for improving spectral efficiency include digital modulation techniques such as frequency-shift keying (FSK), phase-shift keying (PSK), and quadrature amplitude modulation (QAM). Signal multiplexing techniques such as frequency division multiplexing (FDM), time division multiplexing (TDM) and code division multiplexing (CDM) can also be used to improve data rates in a communication system. Of the multiplexing techniques used in modern wired and wireless communications systems, orthogonal FDM achieves the highest bandwidth efficiency (e.g., is closest to the Nyquist rate).
Faster than Nyquist signaling can be possible, but such systems sacrifice orthogonality and inter-symbol interference-free transmission over an additive white Gaussian noise (AWGN) channel are lost. Accordingly, such signaling systems suffer from a compromised signal to noise ratio, and introduce added complexity in the transmitter and receiver. These and other shortcomings are addressed in the present disclosure.